Partially depleted cores are practically ubiquitous in luminous early-type galaxies (MB −20.5 mag) and are typically smaller than 1 kpc. In one popular scenario, supermassive black hole (SMBH) binaries—established during dry (i.e., gas-poor) galaxy mergers—kick out the stars from a galaxy’s central region via three-body interactions. Here, this “binary black hole scouring scenario” is probed at its extremes by investigating the two galaxies reported to have the largest partially depleted cores found to date: 2MASX J09194427+5622012 and 2MASX J17222717+3207571 (the brightest galaxy in Abell 2261). We have fit these galaxy’s two-dimensional light distribution using the core-Sérsic model and found that the former galaxy has a core-Sérsic break radius Rb,cS = 0.55 kpc, which is three times smaller than the published value. We use this galaxy to caution that other reportedly large break radii may too have been overestimated if they were derived using the “sharp-transition” (inner core)-to-(outer Sérsic) model. In the case of 2MASX J17222717+3207571, we obtain Rb,cS = 3.6 kpc. While we confirm that this is the biggest known partially depleted core of any galaxy, we stress that it is larger than expected from the evolution of SMBH binaries—unless one invokes substantial gravitational-wave-induced (black hole-)recoil events. Given the presence of multiple nuclei located (in projection) within the core radius of this galaxy, we explored and found support for the alternative “stalled infalling perturber” core-formation scenario, in which this galaxy’s core could have been excavated by the action of an infalling massive perturber.